Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
auto& in = std::cin;
auto& out = std::cout;
int32_t N;
long double height;
long double want = 0;
long double last_x = 0;
template <typename FUNC>
double binary_search_D(double b, double e, FUNC&& f) {
  for (size_t i = 0; i < 1000; ++i) {
    auto mid = (b + e) / 2;
    if (f(mid)) {
      b = mid;
    } else {
      e = mid;
    }
  }
  return b;
}
int main() {
  using std::endl;
  in.sync_with_stdio(false);
  out.sync_with_stdio(false);
  in >> N >> height;
  want = height / 2.0 / N;
  for (int32_t i = 0; i < N - 1; ++i) {
    last_x = binary_search_D(last_x, height, [](long double X) {
      auto s = (last_x + X) / height * (X - last_x) / 2;
      return s <= want;
    });
    if (i != 0) {
      std::cout << ' ';
    }
    std::cout << std::fixed << std::setprecision(12) << last_x;
  }
  std::cout << std::endl;
  return 0;
}